Such a method, which can be applied in principle in medical diagnostics or in materials testing (including the testing of food-stuffs), is known from J. Phys. E: Sci. Instrum., Vol. 18, 1985, pages 354 to 357. With this method, designated the "ratio method", the test object is traversed by a primary beam and the scattered radiation generated in the test object in the relevant area of the primary beam and leaving the test object at an angle of 90.degree. is measured and in fact divided into a Compton component and an elastic scattered-radiation component. From the ratio of the elastic scattered-ratiation component to the Compton component it is possible to deduce the attenuation factor in the said area of the primary beam.
The separate determination of Compton scattered radiation and elastic scattered radiation utilizes the fact that in a Compton scattering process the energy of an X-ray quantum decreases whilst in elastic scattering (so-called Rayleigh scattering) the scattered X-ray quantum does not undergo any change of energy. To enable Compton scattered radiation and elastic scattered radiation to be distinguished from one another, the amplitude of the pulses generated by the arrival of the X-ray quanta, which is proportional to the energy of the X-ray quanta, has to be determined and evaluated by means of a pulse-height analyser and to make that in fact possible, monochromatic X-radiation has to be used. Radiation sources for monochromatic X-radiation, however, are of essentially lower intensity than radiation sources for polychromatic X-radiation. Additionally, the scattering angle which the scattered radiation detected during measurement makes with the primary beam has to be relatively large--e.g. 90.degree.--so that the energy difference between the elastic scattered radiation and the Compton radiation can be evaluated. With such large scattering angles, however, the intensity of the elastically scattered radiation is very low, while elastically scattered radiation is concentric in the forward direction if the radiation energy is sufficiently high (60 keV) in order to penetrate typical objects. For the reasons stated extremely long measuring times are required in order to achieve sufficiently accurate results.